Flow Lines and Algebraic Invariants in Contact Form Geometry

Preface * Introduction, Statement of Results, Discussion of the Related Hypotheses * Review of the Previous Results, Some Open Questions * Intermediate Section * True Critical Points at Infinity * Removal of (A5) * Conditions (A2) - (A3) - (A4) - (A6) * Bibliography * Index

"The approach of the author. . . has led him throughout the years to the introduction of several new concepts, such as true and false critical points at infinity and cones associated to such points, as well as the introduction of novel algebraic tools, and to the discovery of several interesting phenomena. The monograph under review gives an account of all that. It discusses with a passionate style a number of results, also providing suggestions for further research." -Mathematical Reviews

"This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact cohomology)... Fully detailed, explicit proofs and a number of suggestions for further research are provided throughout." -L'enseignement Mathématique

"In this monograph the author introduces some new methods with the purpose of extracting information about the dynamics of a Hamiltonian system on an energy hypersurface of contact type. His approach is very natural because he employs variational and Morse theoretic methods based on the original variational problem in contrast to the elliptic PDE methods commonly used.... [I]n this reviewer's opinion, the author's approach is very original and interesting: The pseudoholomorphic curve methods commonly used have their origins in the same variational problem as the author's construction. Therefore, there should be a relation between the material in this monograph and constructions stemming from pseudoholomorphic curves, and it would be very interesting to explore their nature." -SIAM Review

"This monograph is related to two previous ones Pseudo-Orbits of Contact Forms, and Classical and Quantic Periodic Motions of Multiply Polorized Spin-Particles, both by the same author. It is a new attempt to create a new tool (rooted in the concept of critical points at infinity) for the study

"The approach of the author. . . has led him throughout the years to the introduction of several new concepts, such as true and false critical points at infinity and cones associated to such points, as well as the introduction of novel algebraic tools, and to the discovery of several interesting phenomena. The monograph under review gives an account of all that. It discusses with a passionate style a number of results, also providing suggestions for further research."   -Mathematical Reviews

"This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact cohomology)... Fully detailed, explicit proofs and a number of suggestions for further research are provided throughout."   -L'enseignement Mathématique

"In this monograph the author introduces some new methods with the purpose of extracting information about the dynamics of a Hamiltonian system on an energy hypersurface of contact type. His approach is very natural because he employs variational and Morse theoretic methods based on the original variational problem in contrast to the elliptic PDE methods commonly used.... [I]n this reviewer's opinion, the author's approach is very original and interesting: The pseudoholomorphic curve methods commonly used have their origins in the same variational problem as the author's construction. Therefore, there should be a relation between the material in this monograph and constructions stemming from pseudoholomorphic curves, and it would be very interesting to explore their nature."   -SIAM Review